Mathematics(Help.......plz)

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(a - b)(a b)(a^2 - b^2)(a^4 - b^4)(a^8 - b^8)(a^16 - b^16).......(a^1024 - b^1024)

Since,
(a-b)(a b) = a^2 b^2
Then,
(a^2 b^2)(a^2 - b^2) = (a^2)^2 (b^2)^2 = a^4 b^4
Therefore,
(a^1024 b^1024)(a^1024 - b^1024) = (a^1024)^2 (b^1024)^2 = a^2048 b^2048

So, the answer should be a^2048 b^2048


Hope that it could be helpful.

2010-07-30 21:06:08 補充：
唔好意思由於電腦出現了小問題,之前打的答案少咗D符號。

Since,
(a-b)(a+b) = a^2 + b^2
Then,
(a^2 + b^2)(a^2 - b^2) = (a^2)^2 + (b^2)^2 = a^4 + b^4
Therefore,
(a^1024 + b^1024)(a^1024 - b^1024) = (a^1024)^2 + (b^1024)^2 = a^2048 + b^2048

So, the answer should be a^2048 + b^2048

希望以上的解釋對你有幫助~

a^2048 - b^2048

Are you sure the question is right? I think the question should be:

(a - b)(a+ b)(a^2 - b^2)(a^4 - b^4)(a^8 - b^8)(a^16 - b^16).......(a^1024 - b^1024)

If that's the case, then it is easy because:

(a-b)(a+b) = a^2 + b^2
(a^2 + b^2)(a^2 - b^2) = a^4 + b^4
.
.
.
(a^1024 + b^1024)(a^1024 - b^1024) = a^2048 + b^2048

Answer is a^2048 + b^2048.